Sec 135 Degrees

The value of Sec 135 degrees is -1.4142135. . .. Sec 135 degrees in radians is written as sec (135° × π/180°), i.e., sec (3π/4) or sec (2.356194. . .). In this article, we will discuss the methods to find the value of sec 135 degrees with examples.

• Sec 135°: -√2
• Sec 135° in decimal: -1.4142135. . .
• Sec (-135 degrees): -1.4142135. . . or -√2
• Sec 135° in radians: sec (3π/4) or sec (2.3561944 . . .)

What is the Value of Sec 135 Degrees?

The value of sec 135 degrees in decimal is -1.414213562. . .. Sec 135 degrees can also be expressed using the equivalent of the given angle (135 degrees) in radians (2.35619 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 135 degrees = 135° × (π/180°) rad = 3π/4 or 2.3561 . . .
∴ sec 135° = sec(2.3561) = -√2 or -1.4142135. . .

Explanation:

For sec 135 degrees, the angle 135° lies between 90° and 180° (Second Quadrant). Since secant function is negative in the second quadrant, thus sec 135° value = -√2 or -1.4142135. . .
Since the secant function is a periodic function, we can represent sec 135° as, sec 135 degrees = sec(135° + n × 360°), n ∈ Z.
⇒ sec 135° = sec 495° = sec 855°, and so on.
Note: Since, secant is an even function, the value of sec(-135°) = sec(135°).

Methods to Find Value of Sec 135 Degrees

The secant function is negative in the 2nd quadrant. The value of sec 135° is given as -1.41421. . .. We can find the value of sec 135 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sec 135° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec 135 degrees as:

• ± 1/√(1 - sin²(135°))
• ± √(1 + tan²(135°))
• ± √(1 + cot²(135°))/cot 135°
• ± cosec 135°/√(cosec²(135°) - 1)
• 1/cos 135°

Note: Since 135° lies in the 2nd Quadrant, the final value of sec 135° will be negative.

We can use trigonometric identities to represent sec 135° as,

• -sec(180° - 135°) = -sec 45°
• -sec(180° + 135°) = -sec 315°
• cosec(90° + 135°) = cosec 225°
• cosec(90° - 135°) = cosec(-45°)

Sec 135 Degrees Using Unit Circle

To find the value of sec 135 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 135° angle with the positive x-axis.
• The sec of 135 degrees equals the reciprocal of the x-coordinate(-0.7071) of the point of intersection (-0.7071, 0.7071) of unit circle and r.

Hence the value of sec 135° = 1/x = -1.4142 (approx)

☛ Also Check:

• sec 11 degrees
• sec 47 degrees
• sec 450 degrees
• sec 28 degrees
• sec 15 degrees
• sec 420 degrees

FAQs on Sec 135 Degrees

What is Sec 135 Degrees?

Sec 135 degrees is the value of secant trigonometric function for an angle equal to 135 degrees. The value of sec 135° is -√2 or -1.4142 (approx).

What is the Value of Sec 135 Degrees in Terms of Tan 135°?

We know, using trig identities, we can write sec 135° as -√(1 + tan²(135°)). Here, the value of tan 135° is equal to -1.

How to Find Sec 135° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec 135° can be given in terms of other trigonometric functions as:

• ± 1/√(1-sin²(135°))
• ± √(1 + tan²(135°))
• ± √(1 + cot²(135°))/cot 135°
• ± cosec 135°/√(cosec²(135°) - 1)
• 1/cos 135°

☛ Also check: trigonometric table

How to Find the Value of Sec 135 Degrees?

The value of sec 135 degrees can be calculated by constructing an angle of 135° with the x-axis, and then finding the coordinates of the corresponding point (-0.7071, 0.7071) on the unit circle. The value of sec 135° is equal to the reciprocal of the x-coordinate(-0.7071). ∴ sec 135° = -1.4142.

What is the Value of Sec 135° in Terms of Cos 135°?

Since the cosine function is the reciprocal of the secant function, we can write sec 135° as 1/cos(135°). The value of cos 135° is equal to -0.7071.